There are many reasons why you might be getting the 500 Error when trying to login, these include:

- A hacked website (which is a huge possibility, considering that you are using an exploitable Joomla version)
- A changed environment - in other words, your host has changed something in your environment, such as the file paths, and this can affect logins.
- A file/database corruption somewhere on your website.
- An extension that you have installed lately on your website (this is a remote possibility though, since you are using a very old version of Joomla).

It's really hard to tell the exact cause from a distance.

As for migrating the website, it really is, as the previous answered said, a rebuild, which has to be done sooner or later in order to protect your website. It is a hard task that takes some time on large websites (and a lot of planning), but it has to be done at one point.

I would say the environment has changed and is causing these issues. I think your best option is to fix your Joomla installation to adjust to the new environment (since Joomla 1.5 has problems with newer environments). Your ideal option, of course, remains the migration to Joomla 3.x.